2 Answers
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The Wikipedia article on the Six Day War states that Palestinian positions in Gaza opened fire on the Negev settlements of Nirim and Kissufim. This provided the pretext/reason for IDF Chief of Staff Yitzhak Rabin to over-ride the orders of Israeli Defence Minister Moshe Dayan (who had had expressly forbidden entry into the Gaza Strip) and order the 11th Mechanised Brigade under Colonel Yehuda Reshef to enter the Strip. The force was immediately met with heavy artillery fire and fierce resistance from Palestinian forces and remnants of Egyptian forces from Rafah.

I'm not entirely sure how much co-ordination there was between the Arab States themselves, let-alone with the PLO. I certainly can't find any evidence to suggest that the PLO coordinated their attacks on this occasion.

The question of the Egyptian and/or Syrian plan for the war has been going on for half-a-century. There probably were nascent plans for a war against Israel, but the water has been muddied by Soviet misinformation before during and after the war, and by the efforts of all the countries involved to justify their actions, and/or explain why they lost so badly, since the 1967 war.

In any event, the preemptive strikes by the IDF rendered any pre-existing plans the Arab States may or may not have had moot (perhaps Helmuth von Moltke's observation that “No Battle Plan Survives Contact With the Enemy” is particularly appropriate here). Even if the plans had been in place, and the PLO had been aware of them, they could never be put into action.

The PLO is a political organization. The PLA, however, the Palestinian Liberation Army was the military wing of the PLO and was definitely involved in the Six-day war. There are several books which detail the function of the PLA before and during the war, detailing its support in Syria and Egypt, how the PLA took up positions in Gaza as the UNEF troops pulled out, and specifically being placed there at the behest of Egypt, so yes, they were in communication with other Arab states.

Another book, The Sinai Blunder: Withdrawal of the United
Nations Emergency Force Leading to the Six-Day War of June 1967, By
Indar Jit Rikhye obviously focuses on the UNEF withdrawal and
the PLA entering Gaza before the Israeli actions.

Look over some of these sources, and you will get the impression of a definite military force, which was organized, trained and supplied by other Arab states.
(I would clip some quotes, but these works are all recent, so you will have to look them over yourselves. Sorry)